PROPORTION. 1. Proportion: A comparison between two or more categories that maintains a ratio, but uses different numbers to express the ratio.

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1 PROPORTION 1. Proportion: A comparison between two or more categories that maintains a ratio, but uses different numbers to express the ratio. Let say we are going to make jello. When we make jello we mix 2 cups of water with every cup of jello crystals. Therefore the ratio of water to crystals is 2:1. To keep the same proportion, if we increase the amount of water we have to increase the amount of crystals. Likewise if we increase the amount of crystals we have to increase the amount of water. Understanding proportion will enable us to do this while maintaining the same 2:1 ratio. Maintaining this ratio will allow us to make different size solutions of jello, but still maintain the same consistency. Cups of water Cups of jello By using proportion we can fill in the rest of the boxes with results that will produce jello of the same consistency. Using the 2:1 ratio we can set it up as a fraction of 2/1 If they are proportionate 2/1 = 4/2 How do we know if this is true? We cross multiply. We multiply the numerator of the first fraction with the denominator of the second fraction to get one term. Then we multiply the denominator of the first fraction with the numerator of the second fraction to get the second term. If these two terms are equal the two fractions are proportionate. Let s try it with the above problem. The numerator of the first fraction (2) times the denominator of the second fraction (2) equals 4. The denominator of the first fraction (1) times the numerator of the second fraction (4) equals 4. Since the two products are equal we know that the two fractions are proportional.

2 Let s try this with the third case in the table above that says for every 6 cups of water we need 3 cups of jello crytals. If this is proportional then 2/1 = 6/3. 2 X 3 = 6 1 X 6 = 6 The two products are the same so we know they are proportional. Now, what if we know that we are going to use 8 cups of water, but we do not know how many cups of jello crystals to use with it. How can we solve our problem? Let s set it up as a proportion. 2/1 = 8/Y. Y represents the number of cups of jello crystals we need to use. Using our cross multiply method 2 X Y = 2Y and 1 X 8 = 8 Since we want the two batches to be proportional 2Y = 8 and we want to isolate (get alone) Y. Dividing both sides of the equal sign by 2 we get Y on the left and 4 on the right. Since Y = 4, we know that if we have 8 cups of water we need 4 cups of jello crystals. But, what if we have 6 cups of jello crystals and we do not know how many cups of water we need? We solve this using the same general method. Our proportion is now 2/1 = Y/6. Y represents the number of cups of water we need. Using our cross multiply method 2 X 6 = 12 and 1 X Y = 1Y (1Y is the same as Y). Since we want the batches to be proportional Y = 12. Y is already isolated. Therefore we know that if we have 6 cups of jello crystals we need 12 cups of water.

3 We can use this same method to solve any proportional problem. Let s look at a different situation in which the answers may not be as obvious. What if we are going to mix sand and cement in a ratio of 3:5? Buckets of sand Buckets of cement Case 1. We have 10 buckets of cement. 3/5 = Y/10 where Y represents the number of buckets of sand needed. Cross multiply. 3 X 10 = 30 and 5 X Y = 5Y Therefore 5Y = 30 Dividing both sides by 5 results in Y = 6 We need 6 buckets of sand Case 2. We have 9 buckets of sand. 3/5 = 9/Y where Y represents the number of buckets of cement needed. Cross multiply. 3 X Y = 3Y and 5 X 9 = 45 Therefore 3Y = 45 Dividing both sides by 3 results in Y = 15. We need 15 buckets of cement. Case 3. We have 25 buckets of cement. 3/5 = Y/25 where Y represents the number of buckets of sand needed. Cross multiply. 3 X 25 = 75 and 5 X Y = 5Y Therefore 5Y = 75 Dividing both sides by 5 results in Y = 15. We need 15 buckets of sand.

4 Case 4. We have 21 buckets of sand. Assignments 3/5 = 21/Y where Y stands for the number of buckets of cement needed. Cross multiply. 3 X Y =3Y and 5 X 21 = 105 Therefore 3Y = 105 Dividing both sides by 3 results in Y = 35. We need 35 buckets of cement. Solve. Round to the nearest hundredth. 1. 2/3 = X/ /X = 7/ /2.8 = X/ /15 = X/ /X = 25/ /1.2 = 6.4/X 3. X/5 = 12/ /45 = 72/X 13. X/6.25 = 16/ /8 = X/ /X = 144/ X/2.54 = 132/ /8 = 40/X /2.3 = X/ / 0.44 = X/ To make cookies Emily mixes 50 g. of flour with every 20 g. of sugar. A. What is the ratio of the weight of sugar to the weight of flour? B. How many grams of flour are needed to mix with 80 grams of sugar? 17. In a school there are four boys scouts to every three girl scouts. A. What is the ratio of the number of boy scouts to the number of girl scouts? B. If there are 42 girl scouts, how many boy scouts are there? 18. To make biscuits, Lindsay uses 5 cups of flour to 1 cup of milk. A. If she uses three cups of milk, how many cups of flour will she use? B. If she uses 20 cups of flour, how many cups of milk will she use? 19. To make green paint a painter mixed yellow paint and blue paint in the ratio of 3:2. If she used 12 gallons of yellow paint, how much blue paint did she use? 20.Mary mixed syrup, milk, and water in the ratio of 2:3:9 to make a drink. She used 6 cups of syrup. How many cups of drink did she make?

5 21.A sum of money was shared between Susan and Nancy in the ratio of 2:5. Nancy received $36 more than Susan. How much money did Susan receive? 22. The ratio of Peter s money to Paul s money is 5:3. Id Peter has $25, how much money do they have altogether? 23. The ratio of the number of Chinese books to the number of English books in a library is 4:7. There are 2200 Chinese books and English books altogether. How many English books are there? 24. The sides of a triangle are in a ratio of 4:5:6. If the perimeter of the triangle is 60cm, find the length of the shortest side. 25. Length Width Sharon mixed meat with potatoes in the ratio of 7:3 to make 4 kg. of meat loaf. How much meat did she use? 27.Connie mixed lime juice, lemon juice, and water in the ratio of 3:6:7 to make eight liters of drink. How many liters of lime juice did she use?. 28.There are three times as many boys as girls in a school band. If there are 12 girls, how many more boys than girls are there? 29. A cake costs $5.00. It costs twice as much as a pie. What is the cost of 3 pies and 2 cakes?

6 children took part in a fire drill. 5/8 of them were boys. How many girls were there? 31. James spent 2/5 of his money and saved the rest. If he spent $630, how much money did he save? 32. The capacities of three buckets are in the ratio of 3:2:4. If the total capacity of the three buckets is 36 liters, find the capacity of the smallest bucket. 33. In a school 3 out of every 5 students wear glasses. If 220 boys and 260 girls wear glasses, find the total number of students in the school. 34. The ratio of the length of a rectangle to its width is 4:3. If the length is 16 cm, what is the perimeter of the rectangle?